Conker can also run at 720P/1080i verses Mario Galaxy's 480P.
That kinda makes the 30fps vs 60fps argument irrellevent. :P

The original Xbox was the first console we got that gave us a taste of HD gaming.

So many to choose from.

Doom
Panzer dragoon
Wreckless
Splinter cell chaos theory
Ninja gaiden
Project Gotham racing 1/2


Lots of graphical gems on that console.

I can't name just one.

Gran Turismo 4 wants a word with you :) I believe it output in 1080i although it was limited to NTSC versions. Not sure if it supported 720P though. The OG Xbox had much better 480P content though with most games supporting it natively via component. Same with the Gamecube although the cables for them have hit insane prices and PAL units had the 480P output stripped almost entirely...

Wikipedia says Conker is 480p: https://en.wikipedia.org/wiki/List_of_Xbox_games_with_alternate_display_modes

And here I was thinking it was Oddworld: Stranger's Wrath...

Ah. You're right. Wondering where I picked up the idea it being HD from?
I have the Crystal PAL Xbox which uses component, must admit I was spending time looking at mods and stuff earlier today to enable High-Definition.

Grand Turismo 4 isn't rendering the game at 1080i, no PS2 game did.
Outputting a resolution and rendering at a resolution are two very different things.

It's actually being rendered at 640x540, the horizontal lines are tripled and the interlacing means the 540 image ends up being 1080, aka. It's being scaled.
Hence why in some cases you get better imagry when you turn off 1080i on the PS2 and have the game at 480P/Enhanced Definition.

It's certainly not as clear as an Original Xbox game at 720P or 1080i that is actually being rendered and output at those resolutions.

Also the Gamecube can go one step farther than the original Xbox, you can tap directly into the digital source, so you will get an image with far more clarity than what you will ever be able to achieve with Component or Composite.

With that said though, Original Xbox games were far more shader and lighting heavy than the Gamecube, which IMHO gives the Xbox a massive edge during that entire generation.

I'm going with DOA3.

Just in terms of scale of the world I would have to say Morrowind GOTY edition done it for me, just because of the OG Xbox having basically a mid range PC in a box it allowed a large open world game come straight into the console space and played it quite well. I know the PS2 had some open world games but I don't think any on the same scale as Morrowind in terms of going from picking tiny mushrooms and herbs to brew potions to fighting giant monster squid.

How? Via internal modification??

Sort-of.
The Gamecube (The earlier consoles anyway.) had Digital Out.


There are various mods and cables around to tap into that, if it's something you are keen into looking at, there is tons of information floating around.
http://www.nintendolife.com/news/2016/01/hardware_review_we_look_at_a_definitive_gamecube_hdmi_mod

Morrowind was amazing.
And ironically... The Original Xbox managed to handle the PC's pixel shaders too.
When Oblivion was floating around me and a bunch of other people modified Oblivion's shaders and assets to run on Xbox equivalent PC hardware (I.E. Geforce 3, Pentium 3, 128Mb SD Ram.).
And Fallout 3 would have likely been possible as well with some trickery and modification to the VATS system (Otherwise you get no heads on Characters).

In-fact if my Xbox was modded and hacked I would have run it directly on the device itself if it also had the doubling of Ram mod.

I wouldn't have been surprised if Bethesda could have made the game run on the original Xbox at 480P, it's a shame the console wasn't on the market for a year or two longer so we could see it stretch it's legs more whilst the PC transitioned to SM2.0/Direct X 9 effects, most games (Especially multiplats) were held back by the lowest common denominator at the time, the PS2.